Algorithms for multiprocessor scheduling with two job lengths and allocation restrictions

A variant of the High Multiplicity Multiprocessor Scheduling Problem with C job lengths is considered, in which jobs can be processed only by machines not greater than a given index. When C=2, polynomial algorithms are proposed, for the feasibility version of the problem and for maximizing the number of scheduled jobs.     

Elucidating multiprocessors flow shop scheduling with dependent setup times using a twin particle swarm optimization

Particle swarm optimization (PSO) is a novel metaheuristic, which has been applied in a wide variety of production scheduling problems. Two basic characteristics of this algorithm are its efficiency and effectiveness in providing high-quality solutions. In order to improve the traditional PSO, this study proposes the incorporation of a local search heuristic into the basic PSO algorithm. The new, hybrid, metaheuristic is called “twin particle swarm optimization (TPSO)”. The proposed metaheuristic scheme is applied to a flow shop with multiprocessors scheduling problem, which can be considered a real world case regarding the production line. This study, as far as the multiprocessors flow shop production system is concerned, utilizes sequence dependent setup times as constraints. Finally, simulated data confirm the effectiveness and robustness of the proposed algorithm. The data test results indicate that TPSO has potential to replace PSO and become a significant heuristic algorithm for similar problems.     

Two-machine open shop scheduling with secondary criteria

This paper considers two-machine open shop problems with secondary criteria where the primary criterion is the minimization of makespan and the secondary criterion is the minimization of the total flow time, total weighted flow time, or total weighted tardiness time. In view of the strongly NP-hard nature of these problems, two polynomially solvable special cases are given and constructive heuristic algorithms based on insertion techniques are developed. A strongly connected neighborhood structure is derived and used to develop effective iterative heuristic algorithms by incorporating iterative improvement, simulated annealing and multi-start procedures. The proposed insertion and iterative heuristic algorithms are empirically evaluated by solving problem instances with up to 80 jobs.     

相关工件车间调度问题的拓扑算法

针对加工装配型离散制造企业实际生产的特点,提出了一类用于表示工序之间偏序关系的相关工件车间调度问题。为了利用已有的求解表示工序之间的线序关系的传统车间调度算法求解相关工件车间调度问题,设计了一种拓扑算法,该算法能够将工序之间的偏序关系转化为线序关系,将相关工件车间调度问题转化为传统的车间调度问题,通过实证研究,结果表明了拓扑算法是可行和高效的。     

Flow shop scheduling with multiple operations and time lags

A scheduling system is proposed and developed for a special type of flow shop. In this flow shop there is one machine at each stage. A job may require multiple operations at each stage. The first operation of a job on stage j cannot start until the last operation of the job on stage j - 1 has finished. Pre-emption of the operations of a job is not allowed. The flow shop that the authors consider has another feature, namely time lags between the multiple operations of a job. To move from one operation of a job to another requires a finite amount of time. This time lag is independent of the sequence and need not be the same for all operations or jobs. During a time lag of a job, operations of other jobs may be processed. This problem originates from a flexible manufacturing system scheduling problem where, between operations of a job on the same workstation, refixturing of the parts has to take place in a load/unload station, accompanied by (manual) transportation activities. In this paper a scheduling system is proposed in which the inherent structure of this flow shop is used in the formulation of lowerbounds on the makespan. A number of lowerbounds are developed and discussed. The use of these bounds makes it possible to generate a schedule that minimizes makespan or to construct approximate solutions. Finally, some heuristic procedures for this type of flow shop are proposed and compared with some well-known heuristic scheduling rules for job shop/flow shop scheduling.An earlier version of this paper was presented at the First International Conference on Industrial Engineering and Production Management 1993, 2–4 June 1993, Mons, Belgium.     

Supporting soft real-time parallel applications on multiprocessors

The prevalence of multicore processors has resulted in the wider applicability of parallel programming models such as OpenMP and MapReduce. A common goal of running parallel applications implemented under such models is to guarantee bounded response times while maximizing system utilization. Unfortunately, little previous work has been done that can provide such performance guarantees. In this paper, this problem is addressed by applying soft real-time scheduling analysis techniques. Analysis and conditions are presented for guaranteeing bounded response times for parallel applications under global EDF multiprocessor scheduling.     

An improved approximation algorithm for two-machine flow shop scheduling with an availability constraint

We study the problem of scheduling n jobs in a two-machine flow shop where the second machine is not available for processing during a given time interval. A resumable scenario is assumed, i.e., if a job cannot be finished before the down period it is continued after the machine becomes available again. The objective is to minimize the makespan. The best fast approximation algorithm for this problem guarantees a relative worst-case error bound of 4/3. We present an improved algorithm with a relative worst-case error bound of 5/4.     

Preemptive stochastic online scheduling on two uniform machines

This paper addresses a stochastic online scheduling problem in which a set of independent jobs are to be processed by two uniform machines whose speeds are 1 and s(s?1). Each job has a processing time, which is a random variable with an arbitrary distribution, and all the jobs are arriving overtime, which means that no information of the job is known in advance before its arrival. During the processing, jobs are allowed to be preempted and resumed later. The objective is to minimize the sum of expected weighted completion times. In this paper, the optimal policy, named SMPR, is designed for the single-machine preemptive stochastic scheduling problem where jobs have a common arriving time. Based on SMPR, the online approximative policy-UMPR, is devised for the preemptive stochastic online scheduling on two uniform machines. Then, UMPR is proved to have an approximation factor of 2. Furthermore, it is concluded that UMPR could not have a smaller approximation factor than 2, which means 2 is the approximation ratio of UMPR for the two-uniform-machine scheduling problem.     

A new particle swarm optimization for the open shop scheduling problem

This paper presents a new particle swarm optimization (PSO) for the open shop scheduling problem. Compared with the original PSO, we modified the particle position representation using priorities, and the particle movement using an insert operator. We also implemented a modified parameterized active schedule generation algorithm (mP-ASG) to decode a particle position into a schedule. In mP-ASG, we can reduce or increase the search area between non-delay schedules and active schedules by controlling the maximum delay time allowed. Furthermore, we hybridized our PSO with beam search. The computational results show that our PSO found many new best solutions of the unsolved problems.     

A polynomial-time approximation scheme for the two-machine flow shop scheduling problem with an availability constraint

We study the problem of scheduling n preemptable jobs in a two-machine flow shop where the first machine is not available for processing during a given time interval. The objective is to minimize the makespan. We propose a polynomial-time approximation scheme for this problem. The approach is extended to solve the problem in which the second machine is not continuously available.     

基于工件位置交叉算子的车间作业调度算法

交叉算子是遗传算法中最主要的遗传算子,对种群的搜索性能起着重要的作用。基于操作编码的遗传算法多采用两点交叉算子,研究发现这种交叉算子收敛速度慢,容易陷入局部最优解,为此设计了一种基于工件位置的交叉算子,通过试验仿真验证了该算子在收敛速度和求全局最优解上有显著优势。     

Flexible open shop scheduling problem to minimize makespan

This study investigates the static and dynamic versions of the flexible open shop scheduling problem with the goal of minimizing makespan. The asymptotic optimality of the general dense scheduling (GDS) algorithm is proven by the boundedness hypothesis. For large-scale problems, the GDS-based heuristic algorithms are presented to accelerate convergence. For moderate-scale problems, the differential evolution algorithm is employed to obtain high-quality solutions. A series of random experiments are conducted to demonstrate the effectiveness of the proposed algorithms.     

An effective asexual genetic algorithm for solving the job shop scheduling problem

By using the notion of elite pool, this paper presents an effective asexual genetic algorithm for solving the job shop scheduling problem. Based on mutation operations, the algorithm selectively picks the solution with the highest quality from the pool and after its modification, it can replace the solution with the lowest quality with such a modified solution. The elite pool is initially filled with a number of non-delay schedules, and then, in each iteration, the best solution of the elite pool is removed and mutated in a biased fashion through running a limited tabu search procedure. A decision strategy which balances exploitation versus exploration determines (i) whether any intermediate solution along the run of tabu search should join the elite pool, and (ii) whether upon joining a new solution to the pool, the worst solution should leave the pool. The genetic algorithm procedure is repeated until either a time limit is reached or the elite pool becomes empty. The results of extensive computational experiments on the benchmark instances indicate that the success of the procedure significantly depends on the employed mechanism of updating the elite pool. In these experiments, the optimal value of the well-known 10 × 10 instance, ft10, is obtained in 0.06 s. Moreover, for larger problems, solutions with the precision of less than one percent from the best known solutions are achieved within several seconds.     

Two-stage hybrid flow shop with precedence constraints and parallel machines at second stage

This study deals with the two-stage hybrid flow shop (HFS) problem with precedence constraints. Two versions are examined, the classical HFS where idle time between the operations of the same job is allowed and the no-wait HFS where idle time is not permitted. For solving these problems an adaptive randomized list scheduling heuristic is proposed. Two global bounds are also introduced so as to conservatively estimate the distance to optimality of the proposed heuristic. The evaluation is done on a set of randomly generated instances. The heuristic solutions for the classical HFS in average are provably situated below 2% from the optimal ones, and on the other hand, in the case of the no-wait HFS the average deviation is below 5%.     

Finding multiple solutions in job shop scheduling by niching genetic algorithms

The interest in multimodal optimization methods is increasing in the last years. The objective is to find multiple solutions that allow the expert to choose the solution that better adapts to the actual conditions. Niching methods extend genetic algorithms to domains that require the identification of multiple solutions. There are different niching genetic algorithms: sharing, clearing, crowding and sequential, etc. The aim of this study is to study the applicability and the behavior of several niching genetic algorithms in solving job shop scheduling problems, by establishing a criterion in the use of different methods according to the needs of the expert. We will experiment with different instances of this problem, analyzing the behavior of the algorithms from the efficacy and diversity points of view.     

Preemptive scheduling on two parallel machines with a single server

This paper addresses a preemptive scheduling problem on two parallel machines with a single server. Each job has to be loaded (setup) by the server before being processed on the machines. The preemption is allowed in this paper. The goal is to minimize the makespan. We first show that it is no of use to preempt the job during its setup time. Namely, every optimal preemptive schedule can be converted to another optimal schedule where all the setup times are non-preemptively performed on one machine. We then present an algorithm with a tight bound of 4/3 for the general case. Furthermore, we show that the algorithm can produce optimal schedules for two special cases: equal processing times and equal setup times, which are NP-hard in the non-preemptive version.     

A hybrid multi-objective immune algorithm for a flow shop scheduling problem with bi-objectives: Weighted mean completion time and weighted mean tardiness

This paper investigates a novel multi-objective model for a no-wait flow shop scheduling problem that minimizes both the weighted mean completion time and weighted mean tardiness . Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult. This paper presents a new hybrid multi-objective algorithm based on the features of a biological immune system (IS) and bacterial optimization (BO) to find Pareto optimal solutions for the given problem. To validate the performance of the proposed hybrid multi-objective immune algorithm (HMOIA) in terms of solution quality and diversity level, various test problems are examined. Further, the efficiency of the proposed algorithm, based on various metrics, is compared against five prominent multi-objective evolutionary algorithms: PS-NC GA, NSGA-II, SPEA-II, MOIA, and MISA. Our computational results suggest that our proposed HMOIA outperforms the five foregoing algorithms, especially for large-sized problems.     

Decision support tool for multi-objective job shop scheduling problems with linguistically quantified decision functions

This paper presents a new tool for multi-objective job shop scheduling problems. The tool encompasses an interactive fuzzy multi-objective genetic algorithm (GA) which considers aspiration levels set by the decision maker (DM) for all the objectives. The GA's decision (fitness) function is defined as a measure of truth of a linguistically quantified statement, imprecisely specified by the DM using linguistic quantifiers such as most, few, etc., that refer to acceptable distances between the achieved objective values and the aspiration levels. The linguistic quantifiers are modelled using fuzzy sets. The developed tool is used to analyse and solve a real-world problem defined in collaboration with a pottery company. The tool provides a valuable support in performing various what-if analyses, for example, how changes of batch sizes, aspiration levels, linguistic quantifiers and the measure of acceptable distances affect the final schedule.     

Approximation algorithms for shop scheduling problems with minsum objective: A correction

We present a correction to the paper, “Approximation algorithms for shop scheduling problems with minsum objective” (Journal of Scheduling 2002; 5:287–305) by Queyranne and Sviridenko. This correction provides a correct derivation of its 2eρ approximation result. Wenhua Li and Jinjiang Yuan: Project supported by NNSFC (Grant 10371112) and NSFHN (Grant 0411011200). Maurice Queyranne: Supported by research grants from NSERC, the Natural Sciences and Engineering Research Council of Canada.